Answer:
-63
Step-by-step explanation:
The opposite, or additive inverse of a number is found by changing the sign of the number. With the exception of zero, a number and its opposite (additive inverse) sum to zero.
Answer:
D
Step-by-step explanation:
72+21-11=82
82-67=15
Answer:
192?
Step-by-step explanation:
-16 = p ÷ [-3 + (-9)]
-16 × [-3 + (-9)] = p
-16 × - 12 = p
192 = p
Answer:
y(x) = 7e^(5x)
Step-by-step explanation:
The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that
dy/dx = 5y
Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)
Using the above stated law now, we can relate to our equation, saying that
y(x) = y(0) e^(5x)
The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have
y(x) = 7e^(5x)
And that is our needed equation of the curve
A: The center is the mid point of the diameter. So, the center of the circle will be the midpoint of points P and Q. The coordinates of the midpoint are the averaged coordinates of the endpoints.
So, the x-cooardinate of the center is the average of the x-coordinates of P and Q:

Try to do the same thing with the y coordinates, and you'll get the y-coordinate
. This first part will be over, because the circle will be point

B: The radius is exactly half the diameter. So, we find the length of the diameter, and we divide it by 2. To find the length of the diameter, we use the standard formula for the distance between two points:

Divide this length by 2 and you'll get the radius.
C: At this point, we have both the radius and the coordinates of the center. The equation of the circle depends on these two parameters, and it is

Substitute
and
with the coordinates of the center (found in point A.) and
with the radius (found in point B.) and you'll have the equation of the circle.